Question

A rectangular field has an area of $1,764m^2$.

The width of the field is $13m$ more than the length.

What is the perimeter of the field?

Answer 1

Step-1: Find the length and width of the given rectangular field:

Let $ABCD$ be a rectangle with length $l$ and width $w$, then

Area of rectangle $=l\times w$ and

Perimeter of rectangle $=2\left[l+w\right]$ $...\left[1\right]$

$l\times w=1,764$ $...\left[2\right]$ [Given]

$w=(l+13)$ $...\left[3\right]$ [Given]

$\Rightarrow$ $l\times (l+13)=1,764$ [Put $w=(l+13)$ in $\left[2\right]$

$\Rightarrow$ $l^2+13l=1,764$

$\Rightarrow$ $l^2+13l-1,764=0$

$\Rightarrow$$l^2+49l-36l-1,764=0$ [Mid-term splitting]

$\Rightarrow$$l(l+49)-36(l+49)=0$

$\Rightarrow$ $(l+49)(l-36)=0$

$\Rightarrow$ $l=-49$ or $l=36$

But $l\ne -49$ since distance can never be negative.

So $l=36$

Put $l=36$ in $\left[2\right]$

$w=(36+13)$

$=49$

Step-2: Find the perimeter of the rectangular field:

The perimeter of the rectangular field $=2(l+w)$ [ From $\left[1\right]$]

$=2(36+49)$ [Put $l=36$ and $w=49$ ]

$=2\times 85$

$=170$

Hence, the perimeter of the rectangular field is $170m$.